Industry betas: unlevering and relevering

In short

• A single stock's beta is noisy because much of its return variation is diversifiable. A portfolio of comparables gives a beta with a lower standard error and a higher correlation with the market.
• Unlevered beta $\beta_u$ = business (asset) risk without financial leverage: $\beta_u = \beta_{L,Comps}/[1 + (1 - t)(D/MVE)]$, using comparables' averages.
• Relever at the firm's own leverage: $\beta_{L,firm} = \beta_u[1 + (1 - t)(D/MVE)_{firm}]$.
• A levered beta is never below its unlevered beta: $\beta_{L,Comps} \geq \beta_u \leq \beta_{L,firm}$. The adjustment matters most when leverage differs a lot.
• Uses: noisy regression betas, private companies and recent IPOs, and firms that recently changed leverage. Caveat: the comparables must share the firm's asset risk.